A Theory Of Frames?

[sigurdV]

Frame 1: Here we are.(Right?)

 

So: What is a "Frame"?

 

(Definition according to Physics) A frame of reference is a conventional standard of rest relative to which measurements can be made and experiments described.

 

Perhaps "Frame" is an intuitive concept. Always being part of "Mixed Concepts" like,for instance:

 

(Definition) An inertial (or Galilean) frame is one in which spatial relations, as determined by rigid scales at rest in the frame, are Euclidean and in which there exists a universal time in terms of which free particles remain at rest or contiinue to move with constant speed along straight lines.

 

(Special principle of Relativity: Einstein) A frame in uniform translatary motion relative to an inertial frame cannot be distinguished from that inertial frame by any physical experiment whatever.

 

Here, I think, E uses "frame" as short for "inertial frame".

 

There might be other uses for the term as in: I have been framed!

I will set these aside.

 

In this first conclusion it seems to me as if the concept "frame" is similar to and definable by the concepts of number and set...

 

Ther are two reasons for asking, one is that "Relativity" sometimes is used in a vague and not satisfactory manner, the other is that (to my surprise) I am not sure what a "frame" is in general... Are you?

[CraigD]

Frame 1: Here we are.(Right?)

 

So: What is a "Frame"?

 

(Definition according to Physics) A frame of reference is a conventional standard of rest relative to which measurements can be made and experiments described.

 

Perhaps "Frame" is an intuitive concept. Always being part of "Mixed Concepts" like,for

Frame isn’t an intuitive concept in any formal system, mathematical physics or pure mathematics, because formal systems by definition don't have intuitive concepts, only postulates and theorems. Though a definition of “formal system” is hard to state tersely, and likely controversial among people familiar with them, I’ve long liked the one Hofstadter outlined in GEB (which I consider an essential deep read for both the mathematically inclined and disinclined), which I’ll paraphrase here: a formal system is a simple rule for transforming strings of symbols from a an alphabet based on other strings of characters.

 

Rather, in math and mathematical physics, “frame” is a general term, having precise meaning only when adequately qualified, either by audience understanding, context, or adjacent modifiers, such as the “Galilean reference frame” you mention, Sigurd.

[sigurdV]

That clears (I think) the formal side of the concept.

 

But i am still a little curious about it: The word, its uses and history. In Swedish we have it in "Ram" obviously related to "Frame". How old is it? Where was and what was its root? Had Indoeuropeans any use for it... they not only farmed they also framed? ;)

 

Back to Formal business then: On one hand we have English. (A Natural Language) On the other the Formal Languages! And I wonder:

 

Is there a "rift" ?

 

There should be a Translation Principle stating (Or a General Method Guaranteeing) that if a postulate or theorem in a Formal System has a meaning then there is a sentence in English having the same meaning? In short: What makes a Formal System understandable?

 

Surely it cant be as in Mystic Systems... Practice and obedience being the only way?

[sigurdV]

The reason I ask is not that i like reading competent answers to "silly" questions like:

 

Are you sure all meaningful formulas in formal systems have translations in ordinary language?

 

Otherwise it could be the case that unnatural horrors are hiding in, and thereby turning Formal Languages into a last reservation for mythical beasts like Dragons and Goedel Sentences...

 

I hasten to add:

Is it not said that natural languages does not contain Goedel Sentences?!

 

So if a Formal system contains a Goedel sentence, then not all its sentences can be translated into Natural Language, and the Principle of Translation FAILS!

 

I am trying to be reasonable: Goedel himself stated that EITHER there are (Goedel-)sentenses OR The system used is inconsistent!

 

HOW this disjunktion turned into the statement: There ARE G-sentenses! is not obvious to me.Has the consistency of the used system finally been satisfyingly proven?

[sigurdV]

Checking the Final solution of the Liar you will find a finished product, with no unnecessary

sentences(excepting the last one wich though unnecessary is sincerely meant and will stay).

 

In here things are different, processes are going on,some to become parts of an exhibition of Absolutes, Singularities and other Theorethical Beasts. Perhaps readers will find unrelated or unnecessary parts... its like building a house: Until it is finished it is surrounded by scaffolding.

 

Cantors Hypothesis is:(As I translate it): All there is is "F" the frame of all frames, everything else is reflexions.

 

This is not as crazy as it looks at first sight! The upshot is the Reflexive Principle,

that everything said about F can instead be said of an existing frame Fn.

 

Above goes on in my mind when I claim that contrary to general opinion there are Goedel sentences in natural languages... in a certain sense they are not really there since logic demands that they should never be asserted, because they belong to the set of Liar Sentences! (This sentence will not be proven true.)

 

I find myself defending THE Translation Principle, even if im not sure what it really looks like:)

PS Who does know?

[sigurdV]

A small item: In the Encyclopedia of Science. If one looks at the concept "self reference" only examples and no definition is given! For a definition check The final Solution of the Liar Paradox.

[CraigD]

But i am still a little curious about it: The word, its uses and history. In Swedish we have it in "Ram" obviously related to "Frame". How old is it? Where was and what was its root? Had Indoeuropeans any use for it... they not only farmed they also framed? ;)

I don’t know linguistics very much or well, but from various references like this webpage and links from it, get that English’s “frame” and Swedish’s “ram” have the same Germanic origin, which in turn has its origin in the Indo-european “*pr”, from which we get Greek/Latin origin words like “promote” and “progress”, and German/English ones like “from”, from which “frame” comes.

 

“Frame” came around the 11 century to have a Middle English conventional meaning pretty near its most common present-day one, to “gather/put together”, as in the verb usage “frame a building” or “frame a picture”. In physics, then, it has the general meaning of “all the ‘pieces’ needed to describe a model with the laws/postulates of a physical system”.

 

Seguing from linguistic to physics...

 

In modern physics – which we can consider in this context to be physics after Einstein’s theory of special relativity – the key importance of the concept described by the term frame is relativity’s requirement that there be no “privileged” one. So long bodies in two separate inertial frames don’t experience any “fictitious forces”, such as an apparent force opposite that of an acceleration of the frame, their physical laws must be identical, especially the law that the speed of light is constant, regardless of its direction.

 

This “if you put it together the same way, regardless of where you put it together, it’ll work the same” principle conveyed by the term “frame” in physics isn’t explicitly stated in our everyday use of the word, say in carpentry, because situation like carpentry don’t much concern themselves with possible expectations to it. Late 19th century physics, on the other hand, focused on finding a major exception by finding an absolute, privileged inertial frame. Detecting the velocity of a specific frame – for practical purposes, our Earth’s – relative to this absolute one is a way to do this. The Michelson-Morley experiment (1887) was designed and performed to do this, and its demonstration of the impossibility of doing so I consider the birth of modern relativity theory and the death of the idea of a privileged frame.

 

Back to Formal business then: On one hand we have English. (A Natural Language) On the other the Formal Languages! And I wonder:

 

Is there a "rift" ?

There’s certainly a practical difference between generating theorems formally and generating natural language utterances and texts via informal reasoning, which I’m comfortable metaphorically calling a “rift”, and associating (but not equating) with the rift Snow describes in The Two Cultures. Put simply, aided by our familiarity with computers, formal language expressions can be generated easily by simple algorithms – computer programs – while natural reasoning involves complicated processes we can’t fully measure or understand – brains.

 

Whether you see this difference as qualitative or merely quantitative – that is, whether you see the brain as a complicated computer, or something fundamentally different, decides, I think, whether you see a profound philosophical rift between the sort of formal “reasoning” computers do, and the informal kind we brains do. For labeling convenience, we can call people who conclude the brain is a complicated computer “strong AI proponents” – because this conclusion implies that, at least in principle, an ordinary computer program can produce “artificial intelligence” identical in kind to our own – and those who conclude it is not “new mysterians”

 

There should be a Translation Principle stating (Or a General Method Guaranteeing) that if a postulate or theorem in a Formal System has a meaning then there is a sentence in English having the same meaning? In short: What makes a Formal System understandable?

It’s easy to describe a formal system in a natural language – every encyclopedic reference of a well-known formal system, such as this Wikipedia article about TNT does so.

 

In general, short theorems in a formal system are easy to understand, while long ones are difficult. Because most formal systems – in particular, any that implements Peano arithmetic - can generate arbitrarily long theorems. So there are some theorems that can’t be understood, if for no other reason that they’re too long for a human to even read them.

 

I wouldn’t say there’s any “general method” for describing any member of a non-trivial class of things in natural language. One “general principle” I can recall is what cognitive scientists call “correspondence”, meaning that after sufficient “juxtaposition” of an external object – in this case, a statement in a formal language – with an internal state corresponding to a natural language phrase, a person equates them.

 

Surely it cant be as in Mystic Systems... Practice and obedience being the only way?

“Mystic systems” – for example, the Kabbalah – aren’t much related to formal systems like TNT, mostly, I think, because they encourage and rely on intuition and “just knowing” (sometime called gnosis), while ones like TNT prohibit appeals to intuition and “just knowing”.

 

Practice is, I think, important in understanding formal systems.

 

Since formal systems are not about loyalty or governance, I wouldn’t use the word “obedience” to describe how one understands them. “Consensus” and “agreement” come to mind as alternatives to what I suspect you mean by “obedience”, SIgurd. For any written language to be useful, people using it must agree on how to use it, and with what its symbols correspond.

[sigurdV]

A first class pyramid of information! Thanx:)

 

Scientists are careful...me? What was "Ramses" meant to mean? Isnt "ram" a holy word in india? And is "ram"in english related to "frame"... Why care?

 

Back to physics and the age of the universe:

 

I read a thought experiment supposed to show that instanteous signals,were they to exist, in certain circumstances could signal back in time:

 

The space traveling twins Max and Maxine are receeding from one another at 90 percent of light speed, and are presently 1.1 light-years apart. Max in the year 1990 sees, because of the sync shift, that Maxines calenders say 1988 Two full light years behind his own way of telling time. If he sends an instantious signal it always stays in 1990 in his frame but it arrives at Maxine's frame in 1988. Because of the same sync shift effect,Maxine, as she recieves Max's signal in the year 1988, sees that Max's calendars say 1986: from Maxine's point of view, it is Max who is two years behind.If Maxine now returns Max's signal instantaneously, the signal will arrive back ay Max's ship in 1986.Using Maxine as a relay Max is able to signal 4 years back into his own past!

 

It will take some effort convincing me that an instantious signal sent in a frame 1990 can hit another frame in 1988! Such a signal is not "instantaneous", it is travelling backwards in time!

 

Surely a signal is instantaneous if, and only if, the age of the universe, in the event it is sent from and in the event it is recieved in, is the same... Then we speak of the events as being simultaneous.

[LaurieAG]

The space traveling twins Max and Maxine are receeding from one another at 90 percent of light speed, and are presently 1.1 light-years apart. Max in the year 1990 sees, because of the sync shift, that Maxines calenders say 1988 Two full light years behind his own way of telling time. If he sends an instantious signal it always stays in 1990 in his frame but it arrives at Maxine's frame in 1988. Because of the same sync shift effect,Maxine, as she recieves Max's signal in the year 1988, sees that Max's calendars say 1986: from Maxine's point of view, it is Max who is two years behind.If Maxine now returns Max's signal instantaneously, the signal will arrive back ay Max's ship in 1986.Using Maxine as a relay Max is able to signal 4 years back into his own past!

 

If Max and Maxine started from a point and both travelled at 45% of the speed of light in opposite directions why would you expect there to be any difference in what either twin saw?

[LaurieAG]

Hi sigurdV,

 

Surely a signal is instantaneous if, and only if, the age of the universe, in the event it is sent from and in the event it is recieved in, is the same... Then we speak of the events as being simultaneous.

 

The age of the universe is constant at any discrete instance so the problem is with the translation to Euclidian space plus time. Its like a continuum that goes back from zero and also goes forward from zero to infinity instead of going from negative infinity to zero (now) and then to positive infinity.

 

Considering that a Wick Rotation (multiply all t with i, t = it) is used in the transformation of Lorenzian space (time) to Euclidian space (+ time), and the speed of light is constant, surely the current frame must be the same for all bodies in the universe at any discrete time (i.e. now) in Euclidian space + time?

 

This simultaneous frame contains all universal bodies where they are now not where they once were.

[CraigD]

I read a thought experiment supposed to show that instanteous signals,were they to exist, in certain circumstances could signal back in time:

 

The space traveling twins Max and Maxine are receeding from one another at 90 percent of light speed, and are presently 1.1 light-years apart. Max in the year 1990 sees ...

I overlooked this old post, until Laurie replied to it last week :doh:

 

Signaling into one past – “closed timelike curves” in physics-speak – is, at least for me, a hard concept to visualize intuitively, but Sigurd is correct in recalling that special relativity predicts that an instantaneous (or “infinite speed”) signal (know as an ansible) can be used to do it. An infinite speed signal isn’t required, just one faster, by even a small fraction, than the speed of light. There are several ways to form CTCs, but let’s consider only the SR-based one.

 

Not only is it hard for me to visualize this CTC, it’s hard for me to explain it, so I’ll just link to an famous (at least to me) old webpage, Richard Baker’s Sharp Blue: Relativity, FTL and causality, the best explanation I’ve yet read.

 

Note that though, for clarity, Baker uses 4 distinct observers in 2 inertial frames and an ansible, all you really need is 2 observers in 2 different inertial frames who can send and receive a signal via some FTL means. Science knows of no such means, so these kinds of CTCs remain in the realm of thought experiments only. When the occasional experiment, such as Nimtz and Stahlhofen’s 2007 FTIR experiment, or the recent much-in-the-news the OPERA group’s 2011 neutrino speed experiment, hints at a possibly physically real such signal, it’s cause for some excitement for folk who keep this thought experiment in mind.

[sigurdV]

Hmmm... Trying to read theese guys gives me head aches! The discussion is on a level above my competence, but I can see they are honestly trying to enlighten me so I will keep on trying getting enlightened :blink:

 

My interest in physics is relatively new ... I felt like widening my horizonts after finishing a rather difficult and time consuming (30 years) research project in logic (for detail see the final solution of the liar)

 

Relativity seemed at first sight an inviting subject... Hunting for Space and Time after finding Truth... But immediately I got stuck on a circular definition of simultaneity so I retreated to the Michelson Morley experiment... And ...grrrr... stuck there also! So I decided to go back way behind Maxwell... Is it ok to start with Parmenides or should I finish Thales first???

Where IS the beginning of physics? And how long and winding is the path that leads up to relativity?? (Sigh!) :(

[JMJones0424]

Modern physics and relativity originate with the same person, Galileo. I'd suggest you start there, and then through Newton to Maxwell. Einstein's first insight was that what holds with optics must also be true with mechanics, then he applied the equivalence principle to make special relativity fit in a gravitational field. Everything since (in classical mechanics) has been gravy.

 

Relativity has always been one of the cornerstones of modern physics, though over the years we have been able to shed unfounded assumptions that seem obvious at our relatively small scales. After all, when traveling in a car at 50 kph, if you drop a cup a coffee, you expect it to fall in your lap, not to fall backwards at a speed 50 kph. This is relativity.

Edited January 12, 2012 by JMJones0424

[sigurdV]

Good Advice Jones! (if I may shorten ure nick)

 

Looking forward I have some understanding of Galileo and Newton, i think they can be said to invent mechanics... I guess the vortex where my lack of knowledge begins to hurt is with Maxwell.

 

Looking backward I think one should take a quick look at Parmenides through the eyes of Descartes, then we have the first look at the picture of the universe still in use to this day:

 

Four dimensions (including time) all points of the time axis having the same status ...thats to say there is no point of "Now" and nothing ever changes! Add to this the theory of atoms first thought of by Democritos and lets call the result "the Static Universe".

 

Summing up: Mathemathics and Astronomy have ancient roots and are presuppositions for Medieval Science filling the static universe up with mechanics and Termodynamics. (BRB)